Question

consider the quadratic function $y = x^2 + 8x + 6$. (a) rewrite the quadratic in vertex form $y = (x - h)^2 + k$. $y = $

Explanation:

Step1: Complete the square for \(x\) terms

Given \(y = x^2 + 8x + 6\). To complete the square, take the coefficient of \(x\) (which is \(8\)), divide by \(2\) to get \(4\), and square it to get \(16\). So we add and subtract \(16\) in the equation:
\(y = x^2 + 8x + 16 - 16 + 6\)

Step2: Rewrite as a perfect square

The first three terms \(x^2 + 8x + 16\) form a perfect square \((x + 4)^2\). Now simplify the constants:
\(y = (x + 4)^2 - 16 + 6\)
\(y = (x + 4)^2 - 10\)

Answer:

\(y=(x + 4)^2 - 10\)